I had the same disappearing Desktop icons and folders that drove me crazy over several hours. Finally it wasn't a trojan or spyware. Below Microsoft XP support article solved my problem. (mine occured after a graphics card update, program uninstalls and a registery clean-tweak)

All the icons may be missing from your desktop. However, if you open your Desktop folder in Windows Explorer, you can see your desktop icons in that window.

CAUSE

This behavior occurs if the Show Desktop Icons feature is turned off.

If you upgrade a previous version of Windows to Windows XP, and Show Desktop Icons was turned off in the previous Windows version, this setting is maintained, and user icons appear to be missing from the desktop. The Show Desktop Icons setting is ignored in previous versions of Windows if Active Desktop is turned off. In Windows XP, Active Desktop is always turned on and cannot be disabled.

RESOLUTION

To resolve this behavior, SIMPLY turn on the Show Desktop Icons feature: